Erratum: flow control in gas networks: exact controllability to a given demand

We correct a technical error in the paper of Gugat, Herty, Schleper, Math. Methods Appl. Sci. 34 (2011), where a framework for controllability of quasi–linear hyperbolic systems has been studied. The application to the case of gas networks is specified in more detail in the current work. Copyright © 2014 John Wiley & Sons, Ltd.     

Standard signal extraction for analyzing target analytes in real samples with complex matrices

A second‐order method, standard signal extraction was proposed for quantitative analysis of target analytes in the samples with complex matrices by gas chromatography–mass spectrometry. In the method, standard addition was adopted. The data of the pure standard, sample, and spiked sample were used in the calculation. By performing principal component analysis on the data aligned with the measured signals of the sample and standard, the standardized signal that is orthogonal to the signals of interferences in the sample can be extracted. Then, the signal of spiked sample was projected to the standardized signal. The concentration ratio of the target analyte in the sample and spiked sample can be obtained. Finally, the concentration of the target analyte in the sample can be calculated with the added concentration in the spiked sample. Both simulated and experimental data were investigated with the proposed approach, compared with rank annihilation factor analysis. The recoveries of standard addition were found in a range of 99–105%, and the relative standard deviations obtained in three repeated measurements were less than 3%. Results show that the method can accurately estimate the quantitative information of analytes of interest in the presence of interferents and can be applied more widely compared with rank annihilation factor analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Tamely uniform orders

The following two results are proven.

(i) Let G be a finitely generated torsion-free linear group. If every torsion-free section of G is an R-group, then G is soluble of finite rank. Conversely, if G has finite rank, then it has a subgroup of finite index, in which every torsion-free section is an R-group.

Let G be a finitely generated torsion-free soluble group. If in every torsion-free section of G the normalizer of each isolated subgroup is isolated, then G has finite rank. Conversely, if G has finite rank, then it has a subgroup K of finite index such that in every torsion-free section of K the normalizer of each isolated subgroup is isolated.     

Test Sets and Test Rank of a Free Metabelian Lie Algebra

Abstract

We prove that the test rank of a free metabelian Lie algebra L of rank n equals n-1 and a test set of L belongs to the derived subalgebra of L.     

NMR Spectroscopy for Protein Higher Order Structure Similarity Assessment in Formulated Drug Products

Peptide and protein drug molecules fold into higher order structures (HOS) in formulation and these folded structures are often critical for drug efficacy and safety. Generic or biosimilar drug products (DPs) need to show similar HOS to the reference product. The solution NMR spectroscopy is a non-invasive, chemically and structurally specific analytical method that is ideal for characterizing protein therapeutics in formulation. However, only limited NMR studies have been performed directly on marketed DPs and questions remain on how to quantitively define similarity. Here, NMR spectra were collected on marketed peptide and protein DPs, including calcitonin-salmon, liraglutide, teriparatide, exenatide, insulin glargine and rituximab. The 1D ¹H spectral pattern readily revealed protein HOS heterogeneity, exchange and oligomerization in the different formulations. Principal component analysis (PCA) applied to two rituximab DPs showed consistent results with the previously demonstrated similarity metrics of Mahalanobis distance (D_M) of 3.3. The 2D ¹H-¹³C HSQC spectral comparison of insulin glargine DPs provided similarity metrics for chemical shift difference (Δδ) and methyl peak profile, i.e., 4 ppb for ¹H, 15 ppb for ¹³C and 98% peaks with equivalent peak height. Finally, 2D ¹H-¹⁵N sofast HMQC was demonstrated as a sensitive method for comparison of small protein HOS. The application of NMR procedures and chemometric analysis on therapeutic proteins offer quantitative similarity assessments of DPs with practically achievable similarity metrics.     

A weak degeneracy revealing decomposition for the CANDECOMP/PARAFAC model

The CANDECOMP/PARAFAC (CP) model is a well known and frequently used tool for extracting substantial information from a three‐way data array. It has several useful characteristics and usually gives meaningful insights about the underlying structure of the data. However, in some cases it has a ‘strange’ behaviour suffering from the so‐called ‘degenerate solutions’, i.e. solutions where the components show a diverging pattern and are meaningless. Several authors have investigated the causes of degeneracy concluding that the phenomenon is due to a lack of minimum of the loss function. In this paper, we study the degeneracy of CP limiting our attention to the two‐component case. The study is done by introducing a canonical form, called 2DR, which is ‘weakly degeneracy revealing’. On the ground of this framework, degeneracy is studied along with some of the remedies proposed in the literature by using a Tucker3 model having a core in the 2DR form. The analysis gives new insights about the behaviour of the CP model and suggests new ideas on how to deal with degeneracy. Copyright © 2010 John Wiley & Sons, Ltd.     

Growth profile of stimulated Raman anti‐Stokes scattering influenced by fluorescence seeding in liquid‐core optical fiber

We demonstrated the growth profile of stimulated Raman anti‐Stokes scattering (SRS) of carbon disulfide (CS₂) influenced by fluorescence seeding of all‐trans‐β‐carotene and rhodamine‐B (RhB) in liquid‐core optical fiber (LCOF). The pump energy which was needed to build up the first‐order anti‐Stokes radiation of CS₂ solutions with the fluorescence seeding was lower than that of CS₂ solutions without fluorescence seeding because of the fluorescence enhancement effect on the intensity of the first‐order Stokes radiation. The first‐order anti‐Stokes radiation of the RhB solution (10⁻⁸ M ) was built up at a lower pump energy than that of the all‐trans‐β‐carotene solution (10⁻⁶ M ), and the intensity of the first‐order anti‐Stokes radiation of the RhB solution was higher than that of the all‐trans‐β‐carotene solution. Simultaneously, the coupled wave differential equations were obtained by the theoretical derivation, and the growth profile of the first‐order anti‐Stokes radiation was theoretically calculated with and without the fluorescence seeding by these equations. Copyright © 2009 John Wiley & Sons, Ltd.     

Loss reserving using loss aversion functions

This article discusses the determination of risk capital based on “aversion” functions. Aversion functions weigh different outcomes according to perceived severity. Many practical and popular risk measures are usefully viewed in terms of aversion functions including those arising from distortion operators and risk margin loadings. The approach of this paper builds on, unifies, and extends existing disparate approaches discussed in the literature. Analytical and computer generated illustrations are given as well as suggestions for the practical determination of aversion functions.     

Modeling of water surface profile in subterranean channel by differential quadrature method (DQM)

This study, investigates the hydraulic of flow in a subterranean channel headspring. The continuity and momentum equations of flow in porous media considering real conditions were used and the basic equation of flow in a subterranean channel was resulted. This equation is very similar to the spatially varied flow with increasing discharge. An equation, defining the hydraulic parameters of a subterranean channel section was adopted. Then differential quadrature method (DQM), was applied to the equation of flow in subterranean channel, consequently the water surface profile was resulted. To illustrate the rightness of model, the hydraulic parameters of flow in the Gavgard branch of the Joopar Goharriz Qanat were measured and the water surface profile was determined. This water surface profile was compared to the water surface profile computed by the model, which are in good agreement.     

非参数固定效应Panel Data模型的统计推断

本文主要讨论了非参数固定效应Panel data模型的估计与检验问题,首先我们利用Profile最小二乘方法得到了固定效应与非参数部分的估计;接着基于比较原假设与备择假设下模型拟合的残差平方和的思想针对固定效应的检验问题构造了检验统计量,并给出了计算检验p-值的F分布逼近法。